If a zipped file is found during gathering, does MessageStats copy or move the zipped file?
When MessageStats finds a compressed Tracking log, it will copy over the zipped file, extract it and parse it to the database and then delete the files when it is finished.
If you want to save the compressed files after MessageStats has parsed them, enable Local Archiving within MessageStats. This can be found under Tools | Options in the MessageStats console. Select the Tracking Logs Tab and check the check box to 'Enable Local Archiving' and provide a local Archive Path to where the files will be stored.